Determine the values of a and b in the following vectors for the indicated property.
m=<10,a,15> and n=<2,-3,b> and vector m is parallel to vector n.
Thanks in advance!
if they are parallel, then the lengths will be proportional.
10/2 = 5, so the ratios of the other dimensions will also be 5:1
In this case, would a=-15 and b=3?
looks good to me.
To determine the values of a and b that make vector m parallel to vector n, we need to find the relationship between the components of the two vectors.
Two vectors are parallel if and only if their corresponding components are proportional. In other words, if we can find a constant k such that the ratios of the corresponding components are all equal, then the vectors are parallel.
Let's compare the x-components of m and n:
10/2 = a/-3 = 15/b
Simplifying each ratio:
5 = -a/3 = 15/b
To solve for a, we can multiply both sides of the equation by 3:
15 = -a = 15/b
From this, we can see that a must be -15.
Similarly, we can solve for b by multiplying both sides of the equation by b:
5b = 15
Dividing both sides by 5:
b = 3
Therefore, the values of a and b that make vector m parallel to vector n are a = -15 and b = 3.